Non-Smooth and Complementarity-Based Distributed Parameter Systems
Geometric Transformations
This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public.Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.
Differential Equations on Manifolds and Mathematical Physics
Parametrix and localized solutions for linearized equations of gas dynamics.- Laplacians on generalized smooth distributions as C*-algebra multipliers.- C*-algebras generated by dynamical systems, and applications to nonlocal PDO.- The equivariant Atiyah-Patodi-Singer theorem.- Representations of Maslov's canonical operator in a neighborhood of caustics.- Resurgent analysis of singularly perturbed differential systems.- Dual linear programming problem and one-dimensional Gromov minimal fillings.- Complete semiclassical spectral asymptotics for periodic and almost periodic perturbations of constant operators.- Analytic properties of the H繹rmander solution of the wave equation.- Derivations of group algebras and Hohschild cohomology.- Mellin operators in weighted corner Sobolev spaces.- Quantum Hall effect and noncommutative geometry.- Flat vector bundles and open coverings.- A class of Fredholm boundary value problems for the wave equation with conditions on the entire boundary.- Motion of mechanical systems across the singular points.- Large-time decay of solutions to the Kawahara equation.- Applications of the Maslov index to phase reconstruction problems.- The complex homotopy principle of Grauert and Gromov for algebras of pseudo differential operators.- On the Fredholm solvability of operators associated with Morse-Smale diffeomorphisms.- Geometrical model of the one-dimensional double pendulum phase space.- Solutions for a nonlinear elliptic problem involving a variable exponent and measure data in unbounded domains.- Periodic internal layers in reaction-diffusion-advection equations with modular type advection.- Model of protosphera.- Pseudo-differential operators, equations, and elliptic boundary value problems.
Algebra.zip
The second edition of the Algebra.zip series of textbooks. We added more section and exercises which to what we believe would benifits the students.
Math Mammoth Grade 5 Tests and Cumulative Reviews
Math Mammoth Grade 5 Tests and Cumulative Reviews includes consumable student copies of the end-of-chapter tests, the end-of-year test, and additional cumulative review lessons, to match Math Mammoth Grade 5 curriculum.
Rectifiability
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside. This title is also available as open access on Cambridge Core.
Math Mammoth Grade 5-B Worktext
Math Mammoth Grade 5-B Worktext is the second student book in Math Mammoth grade 5 curriculum, meant for the latter half of 5th grade. This is the 2023 edition.The main areas of study in Math Mammoth Grade 5-B worktext are: decimal arithmeticfraction arithmetic (all operations with fractions)geometry: review of angles, area, and perimeter; drawing circles; classifying triangles & quadrilaterals; volume of rectangular prismsChapter 6 continues our study of decimals. The focus is on multiplying decimals by decimals, dividing decimals by decimals, and conversions between measuring units.Chapter 7 covers the addition and subtraction of fractions - another topic of focus for 5th grade, besides decimals. The most difficult topic of this chapter is adding and subtracting unlike fractions, which is done by first converting them to equivalent fractions with a common denominator.In chapter 8, we study the multiplication and division of fractions from various angles.Chapter 9 takes us to geometry, starting with a review of angles and polygons. From there, students will learn to classify triangles and quadrilaterals, and will study the concept of volume in the context of right rectangular prisms (boxes).FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.Very little teacher preparation is required. The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.This is the full-color version of the worktext. Please note that it does not include the answers; they are sold as a separate book.
Discrete Quantum Walks on Graphs and Digraphs
Discrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover's search algorithm. These walks are constructed on an underlying graph, and so there is a relation between properties of walks and properties of the graph. This book studies the mathematical problems that arise from this connection, and the different classes of walks that arise. Written at a level suitable for graduate students in mathematics, the only prerequisites are linear algebra and basic graph theory; no prior knowledge of physics is required. The text serves as an introduction to this important and rapidly developing area for mathematicians and as a detailed reference for computer scientists and physicists working on quantum information theory.
Homological Methods in Banach Space Theory
Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.
The ASQ Certified Six Sigma Black Belt Handbook, Fourth Edition
Fully updated to reflect the 2022 ASQ Certified Six Sigma Black Belt (CSSBB) Body of Knowledge (BoK), The ASQ Certified Six Sigma Black Belt Handbook, Fourth Edition is ideal for candidates studying for the CSSBB examination. This comprehensive reference focuses on the core areas of organization-wide planning and deployment, team management, and each of the DMAIC project phases. The fourth edition of this handbook offers thorough explanations of statistical concepts in a straightforward way. It also reflects the latest technology and applications of Six Sigma and lean tools. Updates you will find in the fourth edition include: New topics and tools, such as return on investment calculations, the roles of coaching and finance in projects, process-decision program charts, interrelationship digraphs, A3 analysis, maturity models, key behavior indicators, and audit MSA A new chapter on risk analysis and managementRevamped statistics sectionsNew tables, figures, and examples to help illustrate key points
Math Mammoth Grade 5-A Worktext
Math Mammoth Grade 5-A Worktext is the student book for the first half of grade 5. This student worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. This is the full-color version of the 2023 edition. Please note: The worktext does not include the answer key. The answer keys for grade 5 are sold in a separate book.The main areas of study in the grade 5-A worktext are: the four operations with whole numbersplace value with large numbers and the judicious use of calculatorproblem solving & simple equationsdecimal arithmeticgraphing and the coordinate gridThe year starts out with a study of whole numbers and their operations. Students get to review multi-digit multiplication and learn long division with two-digit divisors. We also review divisibility and factors from fourth grade, and study prime factorization.In the second chapter, the focus is on large numbers and using a calculator. This is the first time a calculator is introduced in Math Mammoth complete curriculum-thus far, all calculations have been done mentally, or with paper and pencil. I want students to learn to be critical in their use of the calculator and use it with good judgment. Every exercise where calculator use is to be allowed is marked with a little calculator symbol.The third chapter is about equations and problem solving. We study simple equations with the help of a balance and bar models. The main idea is to get students used to the idea of an equation and what it means to solve an equation. Students also do a fair amount of problem solving using the visual bar model.The fourth chapter is about decimals and some of the operations with decimals (the rest will be studied in chapter 6). Fifth grade is the time when students learn all the basic operations with decimals. In this chapter, we focus on place value with decimals, addition and subtraction of decimals, and multiplication and division of decimals by whole numbers. Multiplying decimals by decimals and dividing decimals by decimals is covered in chapter 6.In chapter 5, we study graphing in the coordinate grid, line graphs, and average. Today's world has become increasingly complex with lots of data presented in the media, so our children need a good grasp of statistical graphs to be able to make sense of all of that information.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.Very little teacher preparation is required. The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.The curriculum meets and exceeds the Common Core standards.
Math Mammoth Grade 2 Tests and Cumulative Revisions, International Version (Canada)
Math Mammoth Grade 2 Tests and Cumulative Reviews includes consumable student copies of chapter tests, the end-of-year test, and additional cumulative review lessons to match Math Mammoth Grade 2 curriculum. This is the full-color version.
Logic and Its Applications
Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023.Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.
One-Cocycles and Knot Invariants
One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.
The Big Bang of Numbers
Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing--no matter, no cosmos, not even empty space--could we create a universe using only math? Irreverent, richly illustrated, and boundlessly creative, The Big Bang of Numbers invites us to try.In this new mathematical origin story, mathematician and novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. He reveals the secret lives of real and imaginary numbers, teaches them to play abstract games with real-world applications, discovers unexpected patterns that connect humble lifeforms to enormous galaxies, and explores mathematical underpinnings for randomness and beauty. With evocative examples ranging from multidimensional crochet to the Mona Lisa's asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Mathematics, Suri shows, might best be understood not as something we invent to explain Nature, but as the source of all creation, whose directives Nature tries to obey as best she can.Offering both striking new perspectives for math aficionados and an accessible introduction for anyone daunted by calculation, The Big Bang of Numbers proves that we can all fall in love with math.
Stability and Robustness in Data-Driven Predictive Control
Spray polymerisation has a long time been discussed as a promising process, yet, with little knowledge on cause-and-effect relationships between drying and chemical reactions. This work develops a new single droplet model of combined solution drying and free radical homopolymerisation, based on the method of moments. New, consistent approaches for moments' diffusion and the reaction-diffusion system are derived to ensure conservation. Simulations reveal peculiarities of the process such as that, due to drying, polymerisation happens mostly in bulk and monomer evaporation leads to a poor yield. Various process variants and simulation models are discussed. The impact of process parameters is examined by means of numerical DoEs. The second part presents a novel approach for the simulation of structure evolution in suspension drying. The meshfree SPH method is used to model the relevant physical effects on a detailed scale during the first and second drying period. New implementations of physical effects are derived: heat and mass transfer based on linear driving forces, an implicit solution of the heat equation, several approaches for crust formation and a new formulation of surface tension by pairwise forces. The formation of dense structures as well as hollow granules can be simulated. Model parameters influence crust formation during the second drying period concerning shape and microporosity and can be interpreted in a physical sense.
Analyzing Mathematical Patterns - Detection & Formulation
The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
Models and Methods for Quantum Condensation and Fluids
The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
Analyzing Mathematical Patterns - Detection & Formulation
The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
International & Multidisciplinary Pedagogy
The book's primary objectives are to welcome you to the abundant and meaningful international and multidisciplinary education discovery journey. You will grow from exposure to other cultures and their practices and I daresay, become better teachers in your local as well as on-line environments. Most every local classroom is multi-cultural as well. The students have different backgrounds and different ways of internalizing information meaningfully.The book will provide practical examples how to design, promote and teach various courses and seminars abroad. Examples are those the author experienced with a specific pedagogical idea that is successful in one system, however, the same concept may face unexpected challenges or fail in another system. Most importantly, the book will focus on applying feedback as vital tools that will guide us to the designing, promoting and teaching mathematics and multidisciplinary courses and seminars. The book's most important goal is to make international and multidisciplinary education accessible to everyone.The book will compare several educational systems as well as their similarities and differences. These include different teaching and learning styles, students' preparation levels, and students' interests and value orientations. The goal is to inspire you to embark on your own innovative discovery journey, seek out multi-cultural and international teaching opportunities and to effectively reach, effectively communicate information and help students learn.
Games Businesses Play
Game theory has come to dominate industrial organization economics, but business strategists continue to debate its usefulness. So far, empirical work on the application of game theory to business strategy has been too limited to force a consensus. As a (partial) remedy, Games Businesses Play uses detailed case studies of competitive interaction to explore the uses and limits of game theory as a tool for business strategists. Because they are analytical rather than descriptive, the case studies are not typical teaching cases. The cases are paired with customized game-theoretic models that cover a wide range of commitment decisions, from short-run commitments such as price to longer-run commitments such as capacity expansion and reduction, product and process innovation, and battles for market share. A variety of quantitative and qualitative techniques are used to test the models' predictions on case data. In addition the book sheds light on a number of other issues important to strategic management, including the resource-based view of the firm and the emergent theory of dynamic capabilities.
Linear Algebra
This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.
International & Multidisciplinary Pedagogy
The book's primary objectives are to welcome you to the abundant and meaningful international and multidisciplinary education discovery journey. You will grow from exposure to other cultures and their practices and I daresay, become better teachers in your local as well as on-line environments. Most every local classroom is multi-cultural as well. The students have different backgrounds and different ways of internalizing information meaningfully.The book will provide practical examples how to design, promote and teach various courses and seminars abroad. Examples are those the author experienced with a specific pedagogical idea that is successful in one system, however, the same concept may face unexpected challenges or fail in another system. Most importantly, the book will focus on applying feedback as vital tools that will guide us to the designing, promoting and teaching mathematics and multidisciplinary courses and seminars. The book's most important goal is to make international and multidisciplinary education accessible to everyone.The book will compare several educational systems as well as their similarities and differences. These include different teaching and learning styles, students' preparation levels, and students' interests and value orientations. The goal is to inspire you to embark on your own innovative discovery journey, seek out multi-cultural and international teaching opportunities and to effectively reach, effectively communicate information and help students learn.
The Logic of Knowledge Bases
The idea of a knowledge base lies at the heart of symbolic or "good old-fashioned" artificial intelligence (GOFAI). A knowledge-based systemdecides how to act by running formal reasoning procedures over a body of explicitly represented knowledge, its knowledge base. The system isnot programmed for specific tasks; rather, it is told what it needs to know, and expected to infer the rest.This book is about the logic of such knowledge bases. It describes in detail the relationship between symbolic representations of knowledge and abstract states of knowledge, exploring along the way, the foundations of knowledge, knowledge bases, knowledge-based systems, and knowledge representation and reasoning. Assuming some familiarity with first-order predicate logic, the book offers a rigorous mathematical model of knowledge that is general and expressive, yet more workable in practice than previous models.The first edition of the book appeared in the year 2000, and since then its model of knowledge has been applied and extended in a number of ways.This second edition incorporates a number of new results about the logic of knowledge bases, including default reasoning, reasoning about actionand change, and tractable reasoning.Hector Levesque is Professor Emeritus in the Department of Computer Science, University of Toronto. Gerhard Lakemeyer is Professor and Chair of the Department of Computer Science, RWTH Aachen University, and Professor (status only) in the Department of Computer Science, University of Toronto.
Logically Speaking. A Festschrift for Marie Duz穩
This Festschrift is in honour of Professor Marie Duz穩, VSB - Technical University of Ostrava. The 16 contributions, authored by 24 colleagues, runthe gamut from foundations in logic and theoretical computer science through philosophical logic, multi-agent systems and theory of communicationto personal recollections. Marie Duz穩 is best known for her profound and extensive work on both the foundations and multiple applications of Transparent Intensional Logic, originally developed by Pavel Tich羸 in the late 1960s. Her work, whether single-authored or co-authored, has appeared in various high-level journals. In 2008 the Rector of her home university granted Marie the award Outstanding Results in the Development of Science and Research.The 2010 monograph Procedural Semantics for Hyperintensional Logic earned Marie and her coauthors the prestigious Award for OutstandingResults of Major Scientific Importance from the Academy of Sciences of the Czech Republic. The major achievements of Transparent IntensionalLogic that Marie has been involved in over the last decade have been compiled into the volume Transparent Intensional Logic: Selected RecentEssays, also published by College Publications.
Stochastic Processes in Cell Biology
Sensing the environment.- Intracellular pattern formation and reaction-diffusion processes.- Statistical mechanics and dynamics of polymers and membranes.- Self-organization and assembly of cellular structures.- Dynamics and regulation of the cytoskeleton.- Bacterial population growth and collective behavior.- Stochastic reaction-diffusion processes.
Neural Networks are Homeomorphisms
This book is an introductory guide for data scientists to learn the mathematical principles behind the most well-known AI algorithms. The author proposes two original theoretical concepts: the accordion theory and the recurrent third iteration theory. He then applies them to real cases. This work covers topics of higher mathematics from algebraic topology and spectral theory to functional analysis and ergodic theory. These concepts are fundamental to understanding AI concepts and algorithms. This deepens both practitioners' and managers' knowledge of mathematical modeling and assists them to engage with specialized literature. More importantly this book will help them to formally write their own ideas and research.
An Elementary Course on Partial Differential Equations
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Study of Linear and Nonlinear Models with Mathematica
The book is devoted to the problems of modeling physical systems and fields using the tools and capabilities of the 'Mathematica' software package. In the process of teaching classical courses in mechanics and mathematical physics, one often has to overcome significant difficulties associated with the cumbersomeness of the mathematical apparatus, which more than once distracts from the essence of the problems under consideration. The use of the 'Mathematica' package, which has a rich set of analytical and graphic tools, makes the presentation of classic issues related to modeling and interpretation of physical processes much more transparent. This package enables the visualization of both analytical solutions of nonlinear differential equations and solutions obtained in the form of infinite series or special functions.The textbook consists of two parts that can be studied independently of each other. The first part deals with the issues of nonlinear mechanics and the theory of oscillations. The second part covers linear problems of classical mathematical physics and nonlinear evolution models describing, inter alia, transport phenomena and propagation of waves. The book contains the codes of programs written in the 'Mathematica' package environment. Supplementary materials of programs illustrating and often complementing the presented material are available on the publisher's website.
Spatial Dynamics Models in the Life Sciences and the Role of Feedback in Robust Developments
Basic mathematical techniques for partial differential equations (PDE) with applications to the life sciences form an integral part of the core curriculum for programs in mathematical biology. Yet, students in such a program with an undergraduate training in biology are typically deficient in any exposure to PDE. This volume starts with simple first order PDE and progresses through higher order equations and systems but with interesting applications, even at the level of a single first order PDE with constant coefficients.Similar to the two previous volumes by the author, another unique feature of the book is highlighting the scientific theme(s) of interest for the biological phenomena being modelled and analysed. In addition to temporal evolution of a biological phenomenon, its limiting equilibrium states and their stability, the possibility of locational variations leads to a study of additional themes such as (signal and wave) propagation, spatial patterning and robustness. The requirement that biological developments are relatively insensitive to sustained environmental changes provides an opportunity to examine the issue of feedback and robustness not encountered in the previous two volumes of this series.
Stochastic Processes in Cell Biology
Introduction.- Random walks and Brownian motion.- Protein receptors and ion channels.- Molecular motors.- Stochastic gene expression and regulatory networks.- Diffusive transport.- Active transport.- The WKB method, path integrals, and large deviations.- Probability theory and martingales.
Cofinally Complete Metric Spaces and Related Functions
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
Geometry of Deep Learning
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems.Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
Advances in Number Theory and Applied Analysis
Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.
Classical Lie Algebras at Infinity
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension.The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Modeling and Simulation of Protein Folding
The book describes a new mathematical model for intracellular protein folding and the implementation of this model in the form of a novel simulation software. Besides, the related biological, chemical, and physical background, important for understanding and rationalization of the proposed model, is outlined, and a short overview of the best-known methods for protein structure prediction and molecular modeling is given. The first chapter provides a general introduction to the problem, characterizes the chemical structure of proteins, and summarizes amino acid properties, including chirality and ionization behavior. After that, the principles of quantum mechanics and their consequences for the molecular structure are described. The discussion goes over to covalent and hydrogen bonding, as well as to electrostatic and van der Waals interactions. Further, some known facts about the three-dimensional structure of proteins and typical conformations of amino acids are outlined, followed by a quick glance at the hydrophobic effect and the interaction of charged groups with the solvent. Later on the focus is shifted to biological aspects, starting with chaperons and assisted protein folding, mentioning prions, which put into question the popular hypothesis about the global energy minimum of any native structure, and continuing with details of protein synthesis in the cell, which constituted the basis for the proposed model. The chapter finishes with a short description of experimental methods for protein structure prediction and with some information about databases for storage of known protein structures.
Geometry of Black Holes
Black holes present one of the most fascinating predictions of Einstein's general theory of relativity. There is strong evidence of their existence through observation of active galactic nuclei, including the centre of our galaxy, observations of gravitational waves, and others. There exists a large scientific literature on black holes, including many excellent textbooks at various levels. However, most of these steer clear from the mathematical niceties needed to make the theory of black holes a mathematical theory. Those which maintain a high mathematical standard are either focused on specific topics, or skip many details. The objective of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.
Mississippi Academic Assessment Program Test Prep
Want to boost your child's Grade 5 math skills and Mississippi MAAP readiness?Lumos' Mississippi MAAP blended program (Workbook + Online Access) helps your child improve scores by 10% or more* in the 2025-26 MAAP assessment through realistic test simulations, targeted skills practice, and AI-powered intervention.This blended program includes: ✓ Practice questions covering 30+ Grade 5 Math skills in pen and paper format✓ Answer keys with detailed explanations in the workbook✓ 2 full-length online practice tests that simulate Mississippi's MAAP✓ Personalized online study plan for targeted practice✓ AI Tutor for clear step-by-step explanations, hints, and instant feedback✓ Online program access codeTrusted by over 1.6 Million students and 200,000 teachers.Reduce your child's MAAP test anxiety using Lumos' Smart Test Prep MethodologyLumos' Smart Test Prep Methodology blends realistic Mississippi test simulations, personalized guidance, and targeted practice to help students get ready for the state test.Students begin with a simulated MAAP test, follow an AI-personalized study plan, practice essential skills, and repeat the cycle-steadily building the skills and confidence they need for the Spring MAAP.Why is Lumos' MAAP Practice Workbook the Smart Choice for 2025-26?✓ Realistic Practice Tests: Two full-length tests that simulate MAAP format, question types, rigor, standards, and pacing✓ Personalized Study Plan: Online Diagnostic Tests generate a personalized study plan for targeted skills practice using the workbook✓ Lumos AI Tutor: A built-in, on-demand AI coach that delivers real-time assistance just like a personal tutor✓ Online Program Access: Features guided practice questions, solved examples, a performance insights dashboard, videos, mind maps, flashcubes, and other engaging test prep resourcesWhy Parents Trust Lumos tedBook for Mississippi MAAP Success?Lumos has a history of delivering measurable results. Its realistic test preparation builds confidence, and the performance reports offer clear insights into strengths and areas for improvement. With Lumos tedBook, families feel assured that their child is fully prepared to succeed on the Mississippi state assessment."This book is awesome-I've bought it two years in a row. We used it to study for the MAAP Math in 4th grade and the MAAP Math in 5th grade, and my child aced both tests with a score of 4. - JesseniaHow Do Teachers Use Lumos tedBook in Their Classroom?Teachers use Lumos tedBook to deliver personalized, standards-aligned practice that reinforces classroom learning. In addition to giving students the opportunity to experience a realistic MAAP simulation, Lumos Teacher Accounts provide access to insightful reports and guided classroom instructions to bridge learning gaps, track progress, and build student confidence for the MAAP assessment. It's ideal for classroom reinforcement, tutoring, or homeschooling.Prepare with confidence-order now and get ready for MAAP success!*10%+ improvement in state assessment scores is based on students who used the program consistently for about 45 minutes per week. Individual results may vary based on usage and completion of practice tests and the study plan.
Protecting Privacy Through Homomorphic Encryption
This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption. This collection of papers represents the combined wisdom of the community of leading experts on Homomorphic Encryption. In the past 3 years, a global community consisting of researchers in academia, industry, and government, has been working closely to standardize homomorphic encryption. This is the first publication of whitepapers created by these experts that comprehensively describes the scientific inventions, presents a concrete security analysis, and broadly discusses applicable use scenarios and markets. This book also features a collection of privacy-preserving machine learning applications powered by homomorphic encryption designed by groups of top graduate students worldwide at the Private AI Bootcamp hosted by Microsoft Research.The volume aims to connect non-expert readers with thisimportant new cryptographic technology in an accessible and actionable way. Readers who have heard good things about homomorphic encryption but are not familiar with the details will find this book full of inspiration. Readers who have preconceived biases based on out-of-date knowledge will see the recent progress made by industrial and academic pioneers on optimizing and standardizing this technology. A clear picture of how homomorphic encryption works, how to use it to solve real-world problems, and how to efficiently strengthen privacy protection, will naturally become clear.
Mississippi Academic Assessment Program Test Prep
Want to boost your child's Grade 4 math skills and Mississippi MAAP readiness?Lumos' Mississippi MAAP blended program (Workbook + Online Access) helps your child improve scores by 10% or more* in the 2025-26 MAAP assessment through realistic test simulations, targeted skills practice, and AI-powered intervention.This blended program includes: ✓ Practice questions covering 30+ Grade 4 Math skills in pen and paper format✓ Answer keys with detailed explanations in the workbook✓ 2 full-length online practice tests that simulate Mississippi's MAAP✓ Personalized online study plan for targeted practice✓ AI Tutor for clear step-by-step explanations, hints, and instant feedback✓ Online program access codeTrusted by over 1.6 Million students and 200,000 teachers.Reduce your child's MAAP test anxiety using Lumos' Smart Test Prep MethodologyLumos' Smart Test Prep Methodology blends realistic Mississippi test simulations, personalized guidance, and targeted practice to help students get ready for the state test.Students begin with a simulated MAAP test, follow an AI-personalized study plan, practice essential skills, and repeat the cycle-steadily building the skills and confidence they need for the Spring MAAP.Why is Lumos' MAAP Practice Workbook the Smart Choice for 2025-26?✓ Realistic Practice Tests: Two full-length tests that simulate MAAP format, question types, rigor, standards, and pacing✓ Personalized Study Plan: Online Diagnostic Tests generate a personalized study plan for targeted skills practice using the workbook✓ Lumos AI Tutor: A built-in, on-demand AI coach that delivers real-time assistance just like a personal tutor✓ Online Program Access: Features guided practice questions, solved examples, a performance insights dashboard, videos, mind maps, flashcubes, and other engaging test prep resourcesWhy Parents Trust Lumos tedBook for Mississippi MAAP Success?Lumos has a history of delivering measurable results. Its realistic test preparation builds confidence, and the performance reports offer clear insights into strengths and areas for improvement. With Lumos tedBook, families feel assured that their child is fully prepared to succeed on the Mississippi state assessment."This book is awesome-I've bought it two years in a row. We used it to study for the MAAP Math in 3rd grade and the MAAP Math in 4th grade, and my child aced both tests with a score of 4. - JesseniaHow Do Teachers Use Lumos tedBook in Their Classroom?Teachers use Lumos tedBook to deliver personalized, standards-aligned practice that reinforces classroom learning. In addition to giving students the opportunity to experience a realistic MAAP simulation, Lumos Teacher Accounts provide access to insightful reports and guided classroom instructions to bridge learning gaps, track progress, and build student confidence for the MAAP assessment. It's ideal for classroom reinforcement, tutoring, or homeschooling.Prepare with confidence-order now and get ready for MAAP success!*10%+ improvement in state assessment scores is based on students who used the program consistently for about 45 minutes per week. Individual results may vary based on usage and completion of practice tests and the study plan.
Numerical Methods and Optimization
This text, covering a very large span of numerical methods and optimization, is primarily aimed at advanced undergraduate and graduate students. A background in calculus and linear algebra are the only mathematical requirements. The abundance of advanced methods and practical applications will be attractive to scientists and researchers working in different branches of engineering. The reader is progressively introduced to general numerical methods and optimization algorithms in each chapter. Examples accompany the various methods and guide the students to a better understanding of the applications. The user is often provided with the opportunity to verify their results with complex programming code. Each chapter ends with graduated exercises which furnish the student with new cases to study as well as ideas for exam/homework problems for the instructor. A set of programs made in Matlab(TM) is available on the author's personal website and presents both numerical and optimization methods.
The Elements of Hawkes Processes
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
Mathematical Puzzle Tales from Mount Olympus
This book uses fascinating tales from Greek Mythology as the background for introducing mathematics puzzles to the general public. A background in high school mathematics will be ample preparation for using this book, and it should appeal to anyone who enjoys puzzles and recreational mathematics.
Foundations of Quantitative Finance Book II: Probability Spaces and Random Variables
Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the advantage these books offer the astute reader.
Fuzzy Natural Logic in IFSA-EUSFLAT 2021
The present book contains five papers accepted and published in the Special Issue, "Fuzzy Natural Logic in IFSA-EUSFLAT 2021", of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference "The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences", which took place in Bratislava (Slovakia) from September 19 to September 24, 2021.Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF-THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented.This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications.
Model and Mathematics: From the 19th to the 21st Century
How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes between 1830 and 1950. Introduction.- Knowing by Drawing: Geometric Material Models in 19th Century France.- Wilhelm Fiedler and his Models-the Polytechnic Side.- Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry.- Modeling Parallel Transport.- The great yogurt project: models and symmetry principles in early particle physics.- Interview with Myfanwy Evans: Entanglements on and Models of Periodic Minimal Surfaces.- The dialectics archetypes / types (universal categorical constructions / concrete models) in the work of Alexander Grothendieck.- 'Analogies, ' 'Interpretations, ' 'Images, ' 'Systems' and 'Models': Some Remarks on the History of Abstract Representation in the Sciences since the Nineteenth Century.- Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking circa 1900.- Thinking with Notations: Epistemic Actions and Epistemic Activities in Mathematical Practice.- Matrices - Compensating the Loss of Anschauung .- Interview with Anja Sattelmacher: Between Viewing and Touching - Models and Their Materiality.- Interview with Ulf Hashagen: Exhibitions and Mathematical Models in the 19th and 20th Centuries.- Interview with Andreas Daniel Matt: Real-Time Mathematics.
